Even/Odd Data Sufficiency Question

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Even/Odd Data Sufficiency Question

by cauzilan » Fri Dec 17, 2010 4:56 pm
If x and y are integers, is xy even?

1.) x = y + 1

2.) x/y is an even integer


The solution says D, that each statement alone is sufficient. Why is this the case and not B, that only 2. is sufficient?

I understand that with consecutive integers (x = y + 1), that one must be odd and one must be even, but doesn't this only hold true if both integers cannot equal 0? In this case, consider y = -1. Then x = 0 and xy = 0, and therefore 1.) should be insufficient.
Source: — Data Sufficiency |

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by Bharat » Fri Dec 17, 2010 5:20 pm
Answer: D (both are sufficient individually).
A product is even if remainder on division by 2 is 0.
Note that according to this definition, 0 is also even (remainder is zero).

I: x = y+1
you are correct that it means if y is even then x is odd (& vice versa).
Hence one of the components is always an even number & thus the product will always be fully divisible by 2 & remainder will always be zero: SUFFICIENT.
[e.g., x=1,y=0; x=5,y=4 etc. ]

II: x/y = even [this means y can not be zero]
at-least x is alway even (because either x=2*y or x = 0), & thus the products is always even: SUFFICIENT.
(examples: x=6,y=3; x=4, y=2 etc.)
Let me know if you have questions.

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by cauzilan » Fri Dec 17, 2010 5:24 pm
That makes sense. Thanks for your help.